Mixed Numbers And Improper Fractions - BBC Bitesize

In this guide

1. Revise
2. Test

Pages

1. Using fractions
2. Ordering fractions
3. Mixed numbers and improper fractions
4. Fraction arithmetic
5. Multiplying and dividing fractions
6. Fraction arithmetic on a calculator
7. Fractions of amounts

Mixed numbers and improper fractions

Find our updated revision resources for GCSE Maths: Mixed numbers and improper fractions , with step-by-step slideshows, quizzes, practice exam questions, and more!

\(2 \frac{1}{2}\) is an example of a mixed number. This is when whole numbers and fractions are written together.

The same fraction can also be shown as an improper fraction, \(\frac{5}{2}\). This is worth the same amount as the mixed number, but does not separate between whole numbers and parts. Improper fractions have numerators which are bigger than the denominators.

Improper fractions are sometimes called top-heavy fractions.

Converting mixed numbers to improper fractions

To turn mixed numbers into improper fractions, look at the denominator of the fraction first. This will be the denominator of the improper fraction.

Example

Turn \(3 \frac{1}{2}\) into an improper fraction.

The fraction in the mixed number has 2 as its denominator, so the improper fraction will also have 2 as its denominator. 3 whole ones are 6 halves. There is also another half left over. In total, this is 7 halves or \(\frac{7}{2}\).

To convert any mixed number to an improper fraction:

1. multiply the whole number by the denominator
2. add on the numerator

\(3 = 3 \times \frac{2}{2} = \frac{6}{2}\) so \(3 \frac{1}{2} = \frac{7}{2}\)

Converting improper fractions to mixed numbers

To convert an improper fraction to a mixed number, work out how many whole numbers there are by dividing the numerator by the denominator. Make the remainder the new numerator and leave the denominator as it was.

Example

Turn \(\frac{7}{5}\) into a mixed number.

\(7 \div 5\) = 1 whole one, and 2 remaining.

Write \(\frac{7}{5}\) as \(1 \frac{2}{5}\).

Mixed numbers and improper fractions are worth the same amount as one another but are written differently. Mixed numbers are made up of a whole number and a separate fraction. Improper fractions do not show whole numbers separately and the numerator is bigger than the denominator. For example, \(3 \frac{1}{4}\) (mixed number) is equal to \(\frac{13}{4}\) (improper fraction).

Next pageFraction arithmeticPrevious pageOrdering fractions

More guides on this topic

• NEW: Whole numbers
• NEW: Order of operations and negative numbers
• NEW: Decimals
• NEW: Converting between fractions, decimals and percentages
• NEW: Higher – How to convert recurring decimals
• NEW: How to round numbers
• NEW: What is accuracy in maths?
• NEW: What are fractions?
• NEW: How to add, subtract, multiply and divide fractions
• NEW: Multiples and factors
• NEW: Highest Common Factor and Lowest Common Multiple
• NEW: Laws of indices
• NEW: Negative and fractional indices
• NEW: Standard form
• NEW: Calculations using standard form
• Whole numbers - Edexcel
• Approximation - Edexcel
• Decimals - Edexcel
• Multiples and factors - Edexcel
• Standard form - Edexcel
• Laws of indices - Edexcel
• Converting between fractions, decimals and percentages - Edexcel
• Surds - Higher - Edexcel
• Financial mathematics - Edexcel

Related links

• Maths: Exam-style questions
• Maths revision resources
• Personalise your Bitesize!
• Jobs that use Maths
• Radio 4: Maths collection
• Save My Exams Subscription
• Quizlet
• Pearson Education
• Just Maths